Zero overhead self-timed iterative logic

ABSTRACT

CMOS domino logic is normally used only in two phases: precharge and logic evaluation. The invention uses a third phase to store data, which allows domino logic gates to be cascaded and pipelined without intervening latches. The inputs to this system must have strictly monotonic transitions during the logic evaluation phase and the precharge signal must be active during only the precharge phase. Furthermore, the pipelined system can feed its output back to the input to form an iterative structure. Such a feedback pipeline is viewed as a &#34;loop&#34; or &#34;ring&#34; of logic which circulates data until the entire computation is complete.

FIELD OF THE INVENTION

This invention relates to digital electronic circuits, and, moreparticularly, to self-timed circuits, including iterative divisionalgorithms. The design technique of the present patent is called"Zero-Overhead Self-timed Iterative Logic," abbreviated ZOSTIL.

BACKGROUND OF THE INVENTION

The timing performance of any system can be judged by one of twomeasures: latency or throughput. The delay from an input to theresulting output is called the latency, and most real world problemsdesire this delay to be minimized. If a system can have severalcomputations in progress at once, then the minimum delay between twosuccessive inputs determines the throughput, which is the maximum datarate at which the system can accept requests for computation.Performance assessed by either of these measures depends on the sum ofthe raw propagation delay through the combinational logic of the desiredfunction plus "other" overhead delays. From a theoretical point of view,the fastest circuit would eliminate all overheads and have circuitdelays due to only the raw combinational logic. The innovations in thispatent reduce the latency overhead in a pipeline to zero. Hence, theZOSTIL innovation will produce functions whose latency attains thetheoretical lower bound, but without requiring the large and costly areaof a full combinational array.

Traditional synchronous circuit design techniques separate combinationallogic from data storage. That is, storage is provided by explicitlatches interposed between sections of combinational logic. This designtechnique has at least four sources of overhead which increase circuitlatency: 1) propagation delay through latches; 2) margin added totolerate clock skew; 3) wasted time in fast stages within the system; 4)maximizing data-dependent delay; and 5) the assumption of worst casetiming of components.

The first source of latency overhead is due to latches because theyintroduce additional delays due to their set-up time and propagationdelays. The minimum cycle time of a synchronous circuit is the sum ofthe latch set-up time, latch propagation delay, and maximumcombinational logic delay. The first innovation in the ZOSTILmethodology is to remove this overhead completely by removing theexplicit latches altogether and making use of the "free" half-latch atthe output of each stage in a CMOS domino chain.

The second source of latency overhead comes from needing to distributethe clock to all latches in the system. Communicating stages must be inagreement as to when the clock edges occur, but wire or driver delayscause clock skew which must be compensated for by adding some margin tothe total clock period. This added margin is also overhead. Previousasynchronous design techniques used handshaking blocks to remove globalclocks and the extra latency overhead due to clock skew by communicatingdata validity locally instead of globally. But these previous techniquesinclude explicit latches, and hence, still had the latency overhead dueto latch propagation delays. Previous techniques also added someoverhead due to the forward directed paths within the handshaking logic.The second ZOSTIL innovation is to insure all control paths operate inparallel with the forward evaluation rather than adding sequentially tothe path.

The third source of latency overhead is due to mismatching of thefunctional sections between the latches. Because the amount of time in aclock period is fixed, it must be set equal to the longest propagationdelay of all of the different functional sections in the system. Thedifference between that maximum and the actual time used by anyfunctional section is overhead because it is wasted time. A self-timeddataflow does not waste this time because it allows data to flow forwardbased on data-driven local control, rather than waiting for clock edges.Although the throughput of a pipeline is still limited by its sloweststage, the latency is improved by letting each state progress as soon asit can.

The fourth source of latency overhead comes from determining criticalpaths in synchronous logic based on the worst-case data values. If thereis a large variance then there is a large performance loss due to thedifference between the average and maximum values of delay. Synchronousdesigners try to adjust transistor sizing to equalize the various pathsthrough a body of logic, but in self-timed systems it is desired tominimize the probabilistic expected value of the delay rather thanminimizing the maximum delay. The third innovation of this patent is tomake use of any known probabilistic distribution of the inputs of eachblock of logic in order to size the transistors in that block tominimize the expected value of the total delay.

The fifth source of latency overhead is the derating used to insureperformance over a range of temperature and voltage levels. Synchronoussystem design must always be based on conservative derated "worst-case"specifications because the system must work at the environmentalextremes. But when the actual conditions are not at the extremes, thedifference between the possible performance and the actual designedperformance is wasted performance. Self-timed components will always runat their maximum speed for the existing conditions and deliver theiroutputs as soon as they are actually finished. By providing completionindication, they allow an enclosing system to make use of the outputsooner than always waiting for the case.

BACKGROUND AND NOMENCLATURE FOR DUAL-MONOTONIC SIGNALS

If A is a dual-monotonic signal, it is be represented by two"sub-signals", called A⁰ and A¹, with the encoding: if both of the wiresare in the same logical state, say low, then the signal A has not yetevaluated; if either A⁰ or A¹ changes state, this communicates thesignal A has finished evaluating, and the state of A is determined bynoting which of the two wires changed. For example, if both A⁰ and A¹have the binary value `0`, then the value of the signal, A, is not yetdetermined. If A¹ transitions to `1`, then the value of A is `1`, whileif A⁰ transitions to `1`, the value of A is `0`. The pair of wires iscalled a dual-monotonic pair because the transitions on the wires mustbe monotonic during evaluation. These transitions are mutuallyexclusive, and either one indicates the evaluation is complete and canbe used by other circuits. In this patent, signal names are italicized,and a "*" is used to indicate logical inversion. Also, each half of adual-monotonic signal will have a superscript of 1 or 0.

BACKGROUND ON DOMINO LOGIC

Monotonic signals can be conveniently generated by CMOS domino logic.Each signal can be in one of three functional phases: 1) precharge orreset, 2) logic evaluation, or 3) data storage. These three phases areshown in FIG. 1, which shows, respectively, a two-input dual-monotonicAND gate and its waveform diagram. During the reset phase, the activelow precharge signal, P*, is active and the A and B signals must beinactive. This causes the precharged nodes X* and Y* to be high, and theQ outputs, to be low. In the logic evaluation phase, either A⁰ or A¹ andeither B⁰ or B¹ will transition high monotonically. If both A¹ and B¹transition high, the AND gate's Q¹ output monotonically transitionshigh, and if either A⁰ and B⁰ go active, the Q⁰ output will go high.During the data storage phase, both A and B signals are forced low, andP* remains inactive. This condition leaves the precharged nodes X* andY* undriven, and capacitance causes them to act as a memory elements sothe outputs, Q¹ and Q⁰, remain in the same state as they were during thelogic evaluation phase. Thus, each domino stage includes a "free"half-latch because no additional transistors and no additional logicdelays are needed to store data.

OVERVIEW OF THE INNOVATIONS

CMOS domino logic is normally used only in two phases: precharge andlogic evaluation. The invention of the present patent uses a third phaseto store data, which allows domino logic gates to be cascaded andpipelined without intervening latches. The inputs to this system musthave strictly monotonic transitions during the logic evaluation phaseand the precharge signal must be active during only the precharge phase.Furthermore, the pipelined system can feed its output back to the inputto form an iterative structure. Such a feedback pipeline is viewed as a"loop" or "ring" of logic which circulates data until the entirecomputation is complete.

The innovation of making use of the temporary storage of a prechargedfunction block allows the explicit latches to be omitted. Each dominostage provides the operation of a half-latch for free. The Reset Controllogic operates completely in parallel with the block evaluation.Completion detection logic in each Reset Control block observes theoutput of the following Function Block to determine when all of itsoutputs have finished evaluating and then instructs its own FunctionBlock to move from the data storage phase to the precharge phase,driving all its outputs to the reset state. When the outputs of thefollowing Function Block subsequently become reset, the Reset Controlturns off the precharge signal for its Function Block, causing it to beready for the data evaluation phase when its next data input actuallyarrives.

By encoding the data in dual-monotonic pairs, there is no forwardhandshake required and thus the control logic is removed from thecritical path of the circuit. This innovative methodology, inconjunction with the first innovation removing the need for explicitlatches, yields a truly zero overhead minimum latency delay path throughpipelined logic.

The ZOSTIL technique includes combining the latch-free circuits andparallel Reset Control into an iterative structure, or "ring." This isparticularly important for arithmetic operations which perform the samebasic function over and over. Example of these type of functions are:multiplication, division, square root, sine, and cosine.

ZOSTIL circuits are robust because, with proper design of the controllogic, they are delay-independent. That is, the circuits will functioncorrectly regardless of the actual delays of the circuit elements.Therefore, calculations involving delays are not necessary to insure thelogical correctness or functionality of the system, but are used only toestimate the performance. This contrasts to synchronous designtechniques which require extensive delay calculations to insure allcomputations within a single logic stage can be performed in one clockcycle. Improper delay estimation may result in a synchronous circuitwhich does not always produce the correct result.

Division algorithms generate a quotient by successive determination ofquotient digits from most significant to least significant. Because eachquotient digit is used in the computation of the next partial remainder,which in turn is required to determine the next quotient digit, divisionis an inherently sequential process. Hence, a pipelined ring designedwith the ZOSTIL technique is ideal for performing arithmetic division.An additional innovation specific to division is to overlap andinterlock stages to allow two remainder computations to occur inparallel. This is accomplished by modifying an algorithm, known as SRTdivision, to perform several small remainder computations in paralleland choose the correct remainder when the quotient digit from theprevious stage is determined. This innovation improves the overalllatency by a factor of two in comparison with the previous algorithms.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be better understood by reviewing thisdescription given with reference to the following drawings:

FIG. 1: Self-Timed Domino Logic AND Gate--This is a schematic of atwo-input dual-monotonic self-timed AND gate constructed in CMOStechnology.

FIG. 2: Precharged Function Blocks--This is a linear pipeline ofprecharged function blocks which also includes logic for completiondetection, which is used to reset the function blocks.

FIG. 3: Datapaths Merging--This is a schematic showing the Control ResetLogic needed to merge two self-timed pipelines.

FIG. 4: Datapaths Splitting--This is a schematic showing the ControlReset Logic needed to split a self-timed pipeline.

FIG. 5: Improving Expected Total Delay--This shows how changing thecircuit topology without changing the function can improve the expectedcircuit performance.

FIG. 6: Logic for Four Stage Self-Timed Ring--This is a four stagepipeline ring of precharged function blocks.

FIG. 7: Dependency Graph for Four Stage Self-Timed Ring--This isdependency graph of the schematic shown in FIG. 7.

FIG. 8: Sequential Data-flow in Ordinary Radix 2 SRT Division--This isschematic showing the dataflow in one stage of previously described SRTdivision algorithm.

FIG. 9: Intra-stage Overlapped Execution of Radix 2 SRT Division--Thisis a schematic showing the improvement in SRT division.

DETAILED DESCRIPTION OF THE INNOVATIONS

This patent develops innovations in asynchronous circuit designtechnique leading to "Zero-overhead Self-timed Iterative Logic,"abbreviated ZOSTIL.

The ZOSTIL Technique

Asynchronous circuits have the potential for avoiding the latencyoverheads of synchronous circuits. By communicating completion statusalong with the data, each processing element can begin to operate ondata as soon as it arrives without waiting for re-synchronization to aglobal clock at every latch.

Previous implementations of asynchronous logic used explicit latches tostore intermediate results. These latches introduce additionalpropagation delay to the circuit's critical path, but do not directlycontribute to the computational function. The first innovation of thispatent is to avoid explicit latches entirely by using CMOS dominofunction blocks as "free" half-latches. This is possible only if thecontrol for the function block precharge makes certain the outputs froma function block have been utilized by all subsequent stages beforeresetting a function block and destroying the data. In order todetermine when succeeding function blocks are finished using the data,it is necessary to construct a completion detector.

A simple OR gate connected to the two wires of each dual-monotonic pairoutput provides a done indicator for each individual signal output froma logic stage. The stage is considered done computing when all of itsdata outputs are individually done. A tree of last-of gates, commonlycalled C-elements, can be used as the completion detector to determinewhen all of the bits in a datapath have changed. Each C-element has theproperty that its output is that of the inputs when they were last thesame. The output of a tree of C-elements will indicate done when all ofthe inputs are done and the output will indicate reset when all of theinputs have reset.

Once the completion signals are generated, they must be used to providethe control for resetting the precharged blocks appropriately. Previousself-timed circuits required both forward and backward handshakes, butthe second innovation of this patent is to completely embed thecompletion indication of the forward data in dual-monotonic pairs and toeliminate the forward handshake. Further, the backward handshake can bedesigned so that it does not affect the forward critical path. For asimple unidirectional data flow, thiss control is a sequence of backwardpointing inverters as shown in FIG. 2. For merging and splittingdatapaths, the control is as shown in FIGS. 3 and 4. None of thesecontrol circuits are in the direct path of the forward flowing data andhence they do not add to the latency of the forward flowing wave ofdata.

The control logic resets each function block before the next wave ofdata comes along and causes the function block to evaluate its outputsagain. As long as the data waves are spaced apart, each data wave willpropagate with latency equal only to the pure combinational delay,without any additional overhead.

If a problem requires repetitive execution of a logical function, thenit is particularly appropriate to build a ring of precharged functionblocks. The function blocks can be the same, or they may implementdifferent functions. The width of the datapath between stages of thering need not be constant. The data in a self-timed ring loops aroundthe ring at the same speed as it could progress through a largecombinational array, but the silicon area of the circuit is muchreduced. A physical analogy to this is a circle of dominoes. The trickis to make the wave of falling dominoes progress around the circlecontinuously at the same speed as it would down a long row of dominoes,and this is accomplished by standing each domino back up after itssuccessor has fallen.

Usually a linear pipeline is judged by the throughput of the stages. Butwhen the stages are connected into a ring to solve a single iterativeproblem, the time it takes to compute the answer is dependent on thelatency through the stages. So having low latency is the importantproperty for the stages in a loop rather than throughput. Zero overheadcontrol logic reduces the latency to the lower bound of strictly thecombinational delay of the function blocks.

Dependency Graps Verifying Zero Overhead

The ZOSTIL technique results in circuits which function correctlyindependent of the actual delays taken by each of the blocks. Thedesigns are thus robust since changes in thee delays will not affect thelogical operation of the circuit. But, the actual delays determine theoverall performance, and relative delays determine which path throughthe circuit is the limiting, or critical, path. The objective of"Zero-overhead" design is to make sure that the performance is limitedonly by the function blocks comprising the desired combinational logic,and hence that the critical path under nominal relative delays does notgo through any control blocks. If the performance analysis shows thecircuit does not achieve zero overhead, then the schematic can bemodified by making the stages more finely grained until zero overheadlatency is achieved.

To insure a design has no overhead due to control, dependency graphs aredrawn to illustrate all possible critical paths. A simple ring and itsdependency graph are shown in FIGS. 6 and 7. The critical cycle time ofdata flowing around the ring will be the longest cyclic path in thegraph. The graph is really a restricted Petri-net and the firing rulesare the same; a node is marked when all of its predecessors have beenmarked.

Adjusting Logic and Transistor Sizing Based on Data Probabilities

Since self-timed cirrcuits accompany data with completion signals,subsequent computations may begin as soon as each data arrives. Since itis not required that processing times are the same, what is reallydesired is that the total expected value of delay is minimized. In caseswhere data values are distributed with equal probability, the expectedvalue is, of course, minimized when the average delay is minimized.However, in some cases, the designer may know that data values will havea particular distribution, and this information can be used to minimizethe total expected value to be better than just the average of all datavalue delays.

Paths that are known to have higher than average usage can be madefaster by shortening the number of logic blocks they contain or bywidening the transistors so that the blocks go faster. For example inFIG. 6, a net improvement in the expected value of delay will result if,by inverting both arms of a multiplexor, an inverter is removed from thearm known to be more frequently chosen, even though this results in aninverter being added to the other arm. Likewise, if some output of ablock must be loaded with transistors beginning two different paths,narrowing the transistors in the frequently chosen path will slow thatpath, but will result in an overall improvement in expected delaybecause the output node which was also part of the frequently chosenpath will be faster due to less loading.

Self-timed SRT Division

Performing division requires making a choice of quotient digits startingwith the most significant, and progressing to the least significant,digits. The quotient digit decision is made as a part of each iterationwhich recomputes the next partial remainder based on the previouspartial remainder and quotient digit. Between each iteration, thepartial remainder is shifted left by the base, or radix r, of the digitsbeing used. Each iteration thus implements

    R.sub.i+1 =rR.sub.i -Dq.sub.i

where R_(i) is the partial remainder output from stage, i, r is theradix, q_(i) is the quotient digit determined from stage, D is theDivisor, and the sequence is initialized with rR_(i) =the Dividend.

In ordinary division, the quotient digits q_(i) are in the set {0, . . ., r-1}, and thee full quotient has only a single valid representationsince each digit position in the quotient has only a single correctrepresentation. Unfortunately, determining the correct digit at eachposition requires comparison of the exact partial remainder, and thismeans the entire partial remainder must be computed before determiningeach quotient digit. This computation requires a completecarry-propagate subtract to generate the partial remainder before eachquotient digit may be selected.

One published algorithm for division is know as the SRT algorithm. Thekey idea of SRT division is to avoid a complete carry propagation ineach iteration by making the set of valid quotient digits redundant byincluding both positive and negative integers in the set {-p, . . . , 0,. . . , p}. The range of quotient digits must have r/2≦p≦r-1. Withredundant quotient digit sets, the final quotient result can berepresented in several different ways, giving a choice of quotientdigits for each position. Any valid representation can always, ofcourse, be converted to the desired irredundant representation bysubtracting the positionally weighted negative quotient digits from thepositionally weighted positive digits. This subtraction requires a carrypropagation, but it is a single operation which needs only to beperformed once for the whole division operation rather than once perstage. Further, in an integrated floating-point chip, this full-lengthcarry-propagate operation could be performed by shipping the quotientresults to a separate part of the chip implementing fastcarry-look-ahead addition.

Since, in SRT division, the quotient set contains digits of both signs,the quotient selection logic for a given position need only use anapproximation of the divisor and partial remainder. This is becausesmall errors may be corrected at a later stage with less significantquotient digits of the opposite sign. Because only an approximation ofthe partial remainder is required at each stage for the selection ofquotient digits, only a small number of the most significant bits of thepartial remainder need to be examined.

The simplest form of SRT division is to use radix r=2 with only threequotient digits: +1, 0, -1. This requires looking at only the top fourbits of remainder at each stage in order to make the correct quotientdigit selection. The ordinary sequential data-flow for each stage ofthis algorithm is shown in FIG. 8. In discrete implementations, higherradices such as r=4 and r=16 have routinely been used.

The probabilistic distribution of quotient digits is not uniform due tothe numerical properties of SRT division. In the radix 2 case, the threequotient digits have probabilities of 42%, 35%, and 23%; and 4% of thetime it is even possible to predict two quotient digits in advance. Thesign bit of the internal partial remainders has a 77% probability ofbeing on, even for uniformly distributed input operands. Thesestatistics are used to speed the more frequently used circuit pathssince the self-timed implementation which can take advantage of theimprovement.

Intra-stage Overlapped Execution Innovation

Prior to this innovation, the steps of the SRT division algorithm havebeen regarded as being purely sequential. In this patent, the stepswithin each stage of the algorithm are overlapped which makes it fasterby allowing additional parallelism. The data flow for this innovation isshown in FIG. 9. Specifically, the partial 4-bit carry-save andcarry-propagate adders for the remainder formation in each stage canoperate in parallel with the previous quotient digit selection and thestage's own divisor multiple multiplexor and 54-bit carry-save adder.One of the inputs to the partial adders used to be the chosen divisormultiple from the previous stage, which required knowing the selectedquotient digit. But if the partial adders operate in paralle, then thequotient digit is not yet determined. Instead, the innovation is toduplicate the partial adders for each of the possible quotient digits,allowing them to begin computation earlier and in parallel, and thenchoose between their results when the quotient digit from the previousstage catches up. Since there are three possible quotient digits, thereneeds to be a path for each possibility. Fortunately, since one of thequotient digits is zero, there need be only two partial carry-saveadders. This innovation trims the average propagation delay per stage byapproximately one-half because the delay is dominated by thecarry-propagate adder, and the intra-stage overlapped execution allowsthe carry-propagate additions in two successive stages to be executingsimultaneously.

The innovation of intra-stage overlapped execution of SRT division canbe combined with the ZOSTIL innovation by self-timing a sequence ofstages, each having the data flow of FIG. 9. This requires using themerge and join constructs presented in FIGS. 3 and 4. A loop of four ofthese stages will repetitively operate as fast as if the logic for thestages were assembled into a prohibitively large combinational array.

What is claimed is:
 1. A zero-overhead self-timed iterative logic circuit utilizing CMOS domino function blocks incorporating a completion detector associated with each said function block for determining that succeeding function blocks are finished using data from said function block, a function block precharge means being responsive to said completion detector to precharge said function block only when the outputs have been utilized by succeeding blocks, whereupon the function block is reset by said precharge means and the data therein is destroyed. 